AMS310 PRETEST 1
practice questions for Test 1
I.
SHORT ANSWER/MULTIPLE CHOICE QUESTIONS.
1.
ALL QUIZ QUESTIONS
Given f(x)= 0.1x for x=1,2,3, 4.
2 (a) What is the value of
μ
x
? (b)
What is the value of
σ
x
?
3.
Given X has Poisson probability distribution with
λ
=3.2, (a)what is the value of
μ
?
(b) What is the value of
σ
2
?
4. Evaluate
∑
=


10
0
2
)!
10
(
!
!
10
)
3
(
x
x
x
x
0.3
x
0.7
10x
.
5.
P(A)= 0.4, P(AB)=0.4, so P(A
B
) =___.
Ans. 0.4.
6.
X has Poisson probability distribution with
λ
= 5. Use Table 2 to find P(X
≥
4).
7.
For a particular course, there are three grades, 0,1,2, 3 and 4, with 4=A etc. The cumulative distribution of the course
grades is as follows: F(4)=1.0, F(3)=0.85, F(2)=0.65, F(1)=0.2 and F(0)=0.1. (a) What is the probability a student will
receive a B? i.e., P(X=3)? (b) What is the probability that he will receive a score of C or less, i.e., P(X
≤
2)?
Ans.(a) 0.20
(b) 0.65
8.
Suppose X takes on values from 0 to 10 with f(0)=0.01 and f(10)= 0.05, then the standard deviation (a)must be less than 10
(b)can equal 10
(c) can equal 0
(d) can be more than 10.
9.
If
A and B are independent,
then
which
of the following is false?
(a) P(AB)=P(A)
(b)P(A
∪
B) < P(A) + P(B)
(c) P(A
∩
B)=P(A)xP(B)
(d) A, B mutually exclusive.
Ans. (D)
10.
Suppose we toss a fair die ie., S={1,2,3,4,5,6}
Let {A}={1,2,4} and let B={1,2, 5} and let C={3,5,6}
The events {A} and
{C} are (a)mutually exclusive and dependent
(b)mutually exclusive and independent
(c)Not mutually exclusive and
independent (d) not mutually exclusive and dependent.
Answer. (a)
II.
Longer problems:
1.
Let F={ a randomly sampled person works on the 1st Floor} and A = {a randomly sampled person has an accident}.
Suppose we are told that 2% of those who work on the first floor have accidents and that 1% of those who don’t work on
the first floor have accidents.
Suppose we are also told that 75% work on the first floor and 25% do not.
(a)Pr(AF)= ___.
(b)Pr(A
∩
F)=
__ (c)Pr(A
∩
F’)=__ (d)Pr (A) =____ (e)Pr(FA)= __
(f) Is having an accident independent of what floor you
work?
Write a sentence indicating where you would like to work
and the
percentages which prove your point.
Ans. (a)
0.02
(b) 0.015
.
(c)0.0025
.
(d) 0.0175
(e) 0.8571 (f) A, F are not independent.
I would not want to work on the first
floor. On the first floor the percentage of individuals
having accidents is 2% as compared for 1% of workers on all
other floors.